Breaking classical convexity in Waring ' s problem : Sums of cubes and quasi-diagonal behaviour

@inproceedings{Wooley2005BreakingCC,
  title={Breaking classical convexity in Waring ' s problem : Sums of cubes and quasi-diagonal behaviour},
  author={Trevor D. Wooley},
  year={2005}
}
The natural interpretation of even moments of exponential sums, in terms of the number of solutions of certain underlying diophantine equations, permits a rich interplay to be developed between simple analytic inequalities, and estimates for those even moments. This interplay is in large part responsible for the remarkable success enjoyed by the Hardy-Littlewood method in its application to numerous problems of additive type. In the absence of such an interpretation, the most effective method… CONTINUE READING

References

Publications referenced by this paper.
Showing 1-10 of 16 references

On Vinogradov's mean value theorem and Weyl sums. Proceedings of the conference on automorphic forms and analytic number theory (Montreal, PQ

  • E. Bombieri
  • 1989
Highly Influential
5 Excerpts

Large improvements in Waring's problem

  • T. D. Wooley
  • Ann. Math. |35, 131-164
  • 1992
Highly Influential
12 Excerpts

A new iterative method in Waring's problem

  • R. C. Vaughan
  • Acta Math. 162, I--71
  • 1989
Highly Influential
14 Excerpts

Further improvements in Waring's problem

  • R. C. Vaughan, T. D. Wooley
  • Acta Math. 174, 147 240
  • 1995
Highly Influential
9 Excerpts

A new iterafive method in Waring's problem, lh J

  • R. C. Vaughan
  • London Math. Soc. (2) 39, 219-230
  • 1989
Highly Influential
12 Excerpts

Further improvements in Waring's problem, II: Sixth powers

  • R. C. Vaughan, T. D. Wooley
  • Duke Math. J. 76, 683-710
  • 1994
1 Excerpt

On Waring's problem for cubes, lh J

  • R. C. Vaughan
  • London Math. Soc. (2) 39, 205 218
  • 1989
2 Excerpts

R . C . Vaughan : A new iterafive method in Waring ' s problem , lh J

  • T. D. Wooley Vaughan
  • 1989

On Waring's problem

  • C. Hooley
  • Acta. Math. 157, 49-97
  • 1986

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